A triangle has corners A, B, and C located at #(2 ,7 )#, #(5 ,3 )#, and #(2 , 4 )#, respectively. What are the endpoints and length of the altitude going through corner C?
1 Answer
The end points of the altitude are
The length is
Explanation:
Find the slope and the equation of the line segment AB
Use the slope and one of the points to find the equation of the line segment AB:
Use the slope of AB to compute the slope of the Altitude.
Use the slope and point C to find the equation of the altitude:
Use equations [1] and [2] to find the x coordinate of the point of intersection:
Use either equation to find the y coordinate; I will use [2]:
The end points of the altitude are
The length of the altitude is the distance between the two points: